Construction of time-frequency representations from moments

Leon Cohen; Patrick Loughlin; Keith Davidson

doi:10.1117/12.740191

25 September 2007 Construction of time-frequency representations from moments

Leon Cohen, Patrick Loughlin, Keith Davidson

Proceedings Volume 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII; 66970B (2007) https://doi.org/10.1117/12.740191
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

Given the moments of a time-frequency distribution, one can, in principle, construct the characteristic function from which one then obtains the distribution by Fourier transformation. However, often one can not find a closed form for the characteristic function and hence one can not obtain the distribution in a direct manner. We formulate the problem of constructing time-frequency representations from moments without first constructing the characteristic function. Our method is based on expanding the distribution in terms of a complete set of functions where the expansion coeficients are dependent directly on the moments. We apply the method to a case where the even moments are manifestly positive which is a necessary condition for obtaining a proper time-frequency representation.

Citation Download Citation

Leon Cohen, Patrick Loughlin, and Keith Davidson "Construction of time-frequency representations from moments", Proc. SPIE 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 66970B (25 September 2007); https://doi.org/10.1117/12.740191

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